(1) Field of the Invention
The present invention relates to a method for measuring mechanical characteristics of viscoelastic materials. More particularly, this invention provides a method for measuring complex Young""s modulus, complex shear modulus, and complex Poisson""s ratio of a viscoelastic material formed as a rod.
(2) Description of the Prior Art
Measuring Young""s modulus and shear modulus of materials is important because these parameters significantly contribute to the static and dynamic response of a structure. Resonant techniques have been used to identify and measure these moduli for many years. These resonant methods are based on comparing the measured eigenvalues of a structure to predicted eigenvalues from a model of the same structure. The model of the structure must have well-defined (typically closed form) eigenvalues for this method to work. Additionally, resonant techniques only allow measurements at natural frequencies.
Comparison of analytical models to measured frequency response functions is another method used to estimate stiffness and loss parameters of a structure. When the analytical model agrees with one or more frequency response functions, the parameters used to calculate the analytical model are considered accurate. If the analytical model is formulated using a numerical method, a comparison of the model to the data can be difficult due to dispersion properties of the materials.
Methods also exist for measuring Young""s modulus that require strain gages to be affixed to the rod. The mounting of strain gages normally requires that the gage be glued to the specimen, which locally stiffens the material. For soft viscoelastic materials, this can have an adverse impact on the estimate of the loss and stiffness. Another method for measuring stiffness and loss is by deforming the material and measuring the resistance to indentation. This method can physically damage the specimen if the deformation causes plastic deformation.
Prior art methods do not provide closed form, non-resonant techniques for measuring complex Young""s modulus and complex shear modulus of a rod that contains a mass on the end when the end mass changes the dynamic response of the system. This system typically arises when an end accelerometer is attached to a rod to measure the rod""s response. Frequently, the mass is large enough that it significantly changes the response of the rod.
It is a general purpose and object of the present invention to provide a method that measures the material properties of a viscoelastic material.
Yet another purpose of this invention is to provide a method for measuring the complex Young""s modulus, complex shear modulus, and complex Poisson""s ratio of a viscoelastic material.
Still another requirement is that the invention must provide a method for measuring the complex Young""s modulus and complex shear modulus of a material at a frequency other than the resonant frequency of the system.
Accordingly, a method for estimating the real and imaginary Poisson""s ratio of a specimen at an excitation frequency is provided. The specimen is first joined to a reciprocating test apparatus at one end with a mass positioned at the other end. The test apparatus reciprocates at the excitation frequency and accelerations are recorded at each end of the specimen. The Young""s modulus is calculated by mathematical manipulation of the recorded accelerations. The specimen is then joined to a reciprocating rotational test apparatus at one end with an rotational inertia positioned at the other end. Accelerations are recorded upon subjecting the specimen to rotational reciprocations at the excitation frequency. The shear modulus is calculated from mathematical manipulations of these accelerations. Poisson""s ratio can be calculated from the Young""s modulus and the shear modulus at the excitation frequency. All of the calculations may be performed giving both real and imaginary values.